Classification of 3+1D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions
Classification of 3+1D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions
复制标题
DOI：
10.1103/physrevx.9.021005
复制
发表时间：
2019-04-10
影响因子：
12.5
通讯作者：
Wen, Xiao-Gang
中科院分区：
文献类型：
--
作者：
Lan, Tian;Wen, Xiao-Gang
拓扑序描述了一类新的零温带隙量子相，它具有多种多体量子纠缠模式。此前，一维和二维空间中的拓扑序已经被系统地理解和分类。本文[与Phys.Rev.X8,021074(2018年)]发展了对三维玻色子系统拓扑序的系统和分类的理解，其中点状和弦状激发的拓扑类型的数量被假设为有限的。我们的系统理解来自于每个3+1维拓扑序的唯一正则边界。我们发现，正则边界上的点状和弦状激发完全可以用一个数学理论来描述--所谓的融合2范畴。这一理论允许我们根据融合2-范畴的子集对玻色系统中的3+1维拓扑序进行分类。这种系统的理解进一步导致了对具有任意有限么正对称性的玻色子和费米子系统中3+1维拓扑序的系统理解。
Topological orders describe a new class of gapped quantum phases of matter at zero temperature, that has various patterns of many-body quantum entanglement. Previously, topological orders in one and two spatial dimensions have been systematically understood and classified. This paper [together with Phys. Rev. X 8, 021074 (2018)] develops a systematic and classifying understanding of topological orders in three-dimensional bosonic systems, where the number of topological types for the pointlike and stringlike excitations is assumed to be finite. Our systematic understanding comes from the unique canonical boundary for each 3 + 1D topological order. We find that the pointlike and stringlike excitations on the canonical boundary are described fully by a mathematical theory-the so-called fusion 2-categories. This theory allows us to classify 3 + 1D topological orders in bosonic systems in terms of a subset of fusion 2-categories. This systematic understanding further leads to a systematic understanding of 3 + 1D topological orders in bosonic and fermionic systems with arbitrary finite unitary symmetry.